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Abstract

This work reports on the first time experimental investigation of temperature field inside silicon substrates under particle-induced near-field focusing at a sub-wavelength resolution. The noncontact Raman thermometry technique employing both Raman shift and full width at half maximum (FWHM) methods is employed to investigate the temperature rise in silicon beneath silica particles. Silica particles of three diameters (400, 800 and 1210 nm), each under four laser energy fluxes of 2.5 × 108, 3.8 ×108, 6.9 ×108 and 8.6 ×108 W/m2, are used to investigate the effects of particle size and laser energy flux. The experimental results indicate that as the particle size or the laser energy flux increases, the temperature rise inside the substrate goes higher. Maximum temperature rises of 55.8 K (based on Raman FWHM method) and 29.3K (based on Raman shift method) are observed inside the silicon under particles of 1210 nm diameter with an incident laser of 8.6 × 108 W/m2. The difference is largely due to the stress inside the silicon caused by the laser heating. To explore the mechanism of heating at the sub-wavelength scale, high-fidelity simulations are conducted on the enhanced electric and temperature fields. Modeling results agree with experiment qualitatively, and discussions are provided about the reasons for their discrepancy.

Fig. 2 Schematic of the experimental setup for near-field heating and temperature probing (not to scale). A sample that is set on a 3-D piezo-actuated nano-stage is located under the focused laser beam from a Raman spectrometer. The sample is a monolayer of silica particles formed on a silicon substrate. The incident laser, which is used as both temperature probing and heating source, is focused on the substrate by the particles. The laser beam is polarized with the strongest intensity along the x-axis. The spot size of the incident laser is about 2 ×4 µm2 in the x-y plane on the sample. The substrate is heated by the laser in a sub-wavelength region (r ~200 nm) right beneath the particles. During the experiment, the laser beam is fixed, and the sample moves vertically in the z direction controlled by the 3-D nano-stage electrically without any touch of the sample and other equipment. The step of movement is 0.53 μm in a range of about 10 μm, covering the laser focal depth. The temperature rise inside the substrate achieves the highest value at the focal spot.

Fig. 4 (a) Calibration for Raman shift and FWHM of silicon against temperature. The slope of the linear fitting for Raman shift against temperature is −0.022 cm−1/K. For FWHM against temperature, it is 0.0082 cm−1/K. (b) A comparison of Raman spectra between bare silicon and silicon under silica particles. The diameter of silica particle is 1210 nm. The solid curves are the Gaussian fittings for the experimental Raman data. The difference of the two straight lines shows that the Raman peak shifts due to temperature rise in near-field heating.

Fig. 5 The relationship between temperature rise in silicon against (a) energy flux of incident laser and (b) diameter of silica particle. The upper figures show the temperature rise assessed based on the Raman FWHM, and the lower figures are based on the Raman shift method.

Fig. 6 Electric field distribution inside the substrates and particles of (a) 400, (b) 800 and (c) 1210 nm diameter. In figures (a), (b) and (c), the upper figures are top view of the substrates beneath the particles, and the lower figures are central cross-section view of the particles and substrates. The amplitude of electric field is equal to the enhancement factor. (d) Electric field inside silicon in the r direction (along the magnetic field direction). (e) Electric field inside silicon in the z direction. At points A, B and C, the amplitude of electric field drops to e−1. The z-axis values of A, B and C are 878, 1094 and 1013 nm, respectively.

Fig. 7 Temperature distributions inside silicon substrates under particles of (a) 400, (b) 800 and (c) 1210 nm diameter. In figures (a), (b) and (c), the upper figures are top view of the substrates beneath the particles, and the lower figures are central cross-section view of the substrates. (d) Temperature profile inside silicon in the radial direction. (e) Temperature profile inside silicon in the vertical direction. The initial temperature of the substrates is 300 K.